Hamna Ashraf¶

8826836¶

Lab Assignment 5¶

Required Libraries:¶

In [ ]:
import numpy as np
from sklearn.model_selection import train_test_split 
from sklearn.linear_model import LinearRegression
from sklearn import metrics
import matplotlib.pyplot as plt
from sklearn import datasets
from sklearn.preprocessing import PolynomialFeatures
import seaborn as sns
from sklearn.pipeline import Pipeline
from sklearn.tree import DecisionTreeRegressor
from sklearn.neighbors import KNeighborsRegressor
from sklearn.model_selection import cross_validate
import pandas as pd

EDA:¶

In [ ]:
diabetes = datasets.load_diabetes(as_frame=True, scaled=False)
data, target = diabetes.data, diabetes.target
data['target'] = target
In [ ]:
data.describe()
Out[ ]:
age sex bmi bp s1 s2 s3 s4 s5 s6 target
count 442.000000 442.000000 442.000000 442.000000 442.000000 442.000000 442.000000 442.000000 442.000000 442.000000 442.000000
mean 48.518100 1.468326 26.375792 94.647014 189.140271 115.439140 49.788462 4.070249 4.641411 91.260181 152.133484
std 13.109028 0.499561 4.418122 13.831283 34.608052 30.413081 12.934202 1.290450 0.522391 11.496335 77.093005
min 19.000000 1.000000 18.000000 62.000000 97.000000 41.600000 22.000000 2.000000 3.258100 58.000000 25.000000
25% 38.250000 1.000000 23.200000 84.000000 164.250000 96.050000 40.250000 3.000000 4.276700 83.250000 87.000000
50% 50.000000 1.000000 25.700000 93.000000 186.000000 113.000000 48.000000 4.000000 4.620050 91.000000 140.500000
75% 59.000000 2.000000 29.275000 105.000000 209.750000 134.500000 57.750000 5.000000 4.997200 98.000000 211.500000
max 79.000000 2.000000 42.200000 133.000000 301.000000 242.400000 99.000000 9.090000 6.107000 124.000000 346.000000

Correlation Matrix:¶

In [ ]:
corr_values = data.corr().round(2)
sns.heatmap(corr_values, annot=True, linewidth=.5)
Out[ ]:
<Axes: >

By checking the correlation matrix, we can see that not all features are strongly co-related with one another. Especially age has a weak correlation with other features.
But there is a somehow a very weak corelation. Therefore, we don't want remove the data that might appear useful for us later.

Checking all feature histograms:¶

In [ ]:
data.hist(figsize=(20,10))
plt.show()

We can clearly see that the data is normally distributted for all the histogram feature plots we have in our data.

In [ ]:
sns.boxplot(diabetes.data)
plt.show()

Based on the boxplots we see above, there are no outliers that would have an impact on our data.

Conclusion: We can consider all features without dropping any of them.

Setting the test set aside:¶

In [ ]:
#Splitting data into training and testing 
X_train, X_test, y_train, y_test = train_test_split(data, target, test_size=0.2, random_state=0)

Polynomial Regression:¶

In [ ]:
degrees = [2,3]
polynomial_models = {}
for degree in degrees:
    model = Pipeline([('polynomial', PolynomialFeatures(degree=degree)),
                        ('linear', LinearRegression())])
    model.fit(X_train, y_train)
    polynomial_models[degree] = model


polynomial_models
Out[ ]:
{2: Pipeline(steps=[('polynomial', PolynomialFeatures()),
                 ('linear', LinearRegression())]),
 3: Pipeline(steps=[('polynomial', PolynomialFeatures(degree=3)),
                 ('linear', LinearRegression())])}

Decision Tree:¶

In [ ]:
depth_tree = [3,4]
decision_models = {}

for depth in depth_tree:
    model = DecisionTreeRegressor(max_depth = depth)
    model.fit(X_train, y_train)
    decision_models[depth] = model

decision_models
Out[ ]:
{3: DecisionTreeRegressor(max_depth=3), 4: DecisionTreeRegressor(max_depth=4)}

KNN:¶

In [ ]:
knn = [3,4]
knn_models = {}

for neighbour in knn:
    model = KNeighborsRegressor(n_neighbors = neighbour)
    model.fit(X_train, y_train)
    knn_models[neighbour] = model

knn_models
Out[ ]:
{3: KNeighborsRegressor(n_neighbors=3), 4: KNeighborsRegressor(n_neighbors=4)}

Cross-Validation:¶

In [ ]:
poly_cv_results = []
scoring = ['r2', 'neg_mean_absolute_error', 'neg_mean_absolute_percentage_error']

for degree,model in polynomial_models.items():
    scores = cross_validate(model, X_train, y_train, scoring=scoring, cv=5)
    poly_cv_results.append(scores)


poly_cv_df = pd.DataFrame(poly_cv_results)

poly_cv_results
Out[ ]:
[{'fit_time': array([0.01618171, 0.02072787, 0.01360106, 0.0147264 , 0.01261258]),
  'score_time': array([0.        , 0.00194693, 0.00200152, 0.00200319, 0.00200057]),
  'test_r2': array([1., 1., 1., 1., 1.]),
  'test_neg_mean_absolute_error': array([-2.52883160e-12, -2.52192633e-12, -5.38010950e-13, -1.37672730e-12,
         -2.09711613e-12]),
  'test_neg_mean_absolute_percentage_error': array([-2.45782101e-14, -2.13014374e-14, -4.75960377e-15, -1.32700835e-14,
         -1.68151579e-14])},
 {'fit_time': array([0.0773468 , 0.06364894, 0.07681632, 0.10416341, 0.07166123]),
  'score_time': array([0.00200176, 0.01268768, 0.00253797, 0.00198841, 0.00200081]),
  'test_r2': array([0.9996872 , 0.99991279, 0.99968212, 0.99927632, 0.99962645]),
  'test_neg_mean_absolute_error': array([-0.750033  , -0.47142892, -0.90228803, -1.15981223, -1.11176176]),
  'test_neg_mean_absolute_percentage_error': array([-0.00586324, -0.00348705, -0.00668015, -0.01068595, -0.00737517])}]
In [ ]:
decision_cv_results = []

for degree, model in decision_models.items():
    scores = cross_validate(model, X_train, y_train, scoring=scoring, cv=5)
    decision_cv_results.append(scores)

decision_cv_df = pd.DataFrame(decision_cv_results)

decision_cv_results
Out[ ]:
[{'fit_time': array([0.00151539, 0.        , 0.        , 0.00307822, 0.        ]),
  'score_time': array([0.        , 0.        , 0.00987434, 0.00012779, 0.        ]),
  'test_r2': array([0.97609543, 0.9773424 , 0.97960509, 0.97881853, 0.97568939]),
  'test_neg_mean_absolute_error': array([-10.15471308,  -9.58869683,  -9.12163469,  -8.97775277,
          -9.86933144]),
  'test_neg_mean_absolute_percentage_error': array([-0.09231926, -0.07573048, -0.09260466, -0.0791138 , -0.08162868])},
 {'fit_time': array([0.        , 0.        , 0.00200558, 0.00284529, 0.        ]),
  'score_time': array([0.        , 0.01261091, 0.00086999, 0.        , 0.        ]),
  'test_r2': array([0.99432178, 0.99375734, 0.99314839, 0.99512337, 0.99389501]),
  'test_neg_mean_absolute_error': array([-4.6590326 , -5.05199369, -5.34047648, -4.49118856, -5.34942623]),
  'test_neg_mean_absolute_percentage_error': array([-0.04218649, -0.04116375, -0.05305009, -0.04198837, -0.04385112])}]
In [ ]:
knn_cv_results = []

for degree, model in decision_models.items():
    scores = cross_validate(model, X_train, y_train, scoring=scoring, cv=5)
    knn_cv_results.append(scores)

knn_cv_df = pd.DataFrame(knn_cv_results)

knn_cv_results
Out[ ]:
[{'fit_time': array([0.0012095 , 0.        , 0.00943065, 0.00235128, 0.        ]),
  'score_time': array([0.        , 0.        , 0.00222421, 0.00044513, 0.        ]),
  'test_r2': array([0.97609543, 0.9773424 , 0.97960509, 0.97881853, 0.97568939]),
  'test_neg_mean_absolute_error': array([-10.15471308,  -9.58869683,  -9.12163469,  -8.97775277,
          -9.86933144]),
  'test_neg_mean_absolute_percentage_error': array([-0.09231926, -0.07573048, -0.09260466, -0.0791138 , -0.08162868])},
 {'fit_time': array([0.        , 0.00314999, 0.00201297, 0.        , 0.00941801]),
  'score_time': array([0.00961733, 0.00200939, 0.        , 0.        , 0.00177574]),
  'test_r2': array([0.99432178, 0.99375734, 0.99314839, 0.99512337, 0.99389501]),
  'test_neg_mean_absolute_error': array([-4.6590326 , -5.05199369, -5.34047648, -4.49118856, -5.34942623]),
  'test_neg_mean_absolute_percentage_error': array([-0.04218649, -0.04116375, -0.05305009, -0.04198837, -0.04385112])}]
In [ ]:
poly_cv_df
Out[ ]:
fit_time score_time test_r2 test_neg_mean_absolute_error test_neg_mean_absolute_percentage_error
0 [0.01618170738220215, 0.020727872848510742, 0.... [0.0, 0.0019469261169433594, 0.002001523971557... [1.0, 1.0, 1.0, 1.0, 1.0] [-2.5288316042143624e-12, -2.521926329740074e-... [-2.4578210077298986e-14, -2.130143742303784e-...
1 [0.0773468017578125, 0.06364893913269043, 0.07... [0.0020017623901367188, 0.01268768310546875, 0... [0.9996871971629486, 0.9999127914287887, 0.999... [-0.7500330025260014, -0.47142891852721874, -0... [-0.005863235936443113, -0.0034870453724598714...
In [ ]:
decision_cv_df
Out[ ]:
fit_time score_time test_r2 test_neg_mean_absolute_error test_neg_mean_absolute_percentage_error
0 [0.0015153884887695312, 0.0, 0.0, 0.0030782222... [0.0, 0.0, 0.009874343872070312, 0.00012779235... [0.9760954318883467, 0.9773424027979054, 0.979... [-10.154713083132828, -9.588696827429219, -9.1... [-0.09231925608184031, -0.07573048359331443, -...
1 [0.0, 0.0, 0.0020055770874023438, 0.0028452873... [0.0, 0.012610912322998047, 0.0008699893951416... [0.9943217844314327, 0.9937573421846522, 0.993... [-4.6590326031865, -5.051993694185866, -5.3404... [-0.042186491138786884, -0.04116375209487312, ...
In [ ]:
knn_cv_df
Out[ ]:
fit_time score_time test_r2 test_neg_mean_absolute_error test_neg_mean_absolute_percentage_error
0 [0.0012094974517822266, 0.0, 0.009430646896362... [0.0, 0.0, 0.0022242069244384766, 0.0004451274... [0.9760954318883467, 0.9773424027979054, 0.979... [-10.154713083132828, -9.588696827429219, -9.1... [-0.09231925608184031, -0.07573048359331443, -...
1 [0.0, 0.0031499862670898438, 0.002012968063354... [0.009617328643798828, 0.0020093917846679688, ... [0.9943217844314327, 0.9937573421846522, 0.993... [-4.6590326031865, -5.051993694185866, -5.3404... [-0.042186491138786884, -0.04116375209487312, ...

Polynomial Plot

In [ ]:
plt.figure(figsize=(20,10))

for degree,model in polynomial_models.items():
    plt.plot(X_train, model.predict(X_train), label='Polynomial Regression',color='#2E8B57')


plt.xlabel('Features')
plt.title('Data Points and Fitted model')
plt.show()

Decision Tree Plot

In [ ]:
plt.figure(figsize=(20,10))

for degree,model in decision_models.items():
    plt.plot(X_train, model.predict(X_train), color='#CD5C5C')



plt.xlabel('Features')
plt.title('Data points and Fitted model')
plt.show()

KNN Plot:

In [ ]:
plt.figure(figsize=(20,10))

for degree,model in knn_models.items():
    plt.plot(X_train, model.predict(X_train), color='#7B68EE')


plt.xlabel('Features')
plt.title('Data points and Fitted model')
plt.show()
In [ ]:
plt.figure(figsize=(20,10))

for degree,model in polynomial_models.items():
    plt.plot(X_train, model.predict(X_train),color='#2E8B57')


for degree,model in decision_models.items():
    plt.plot(X_train, model.predict(X_train), color='#CD5C5C')

for degree,model in knn_models.items():
    plt.plot(X_train, model.predict(X_train),color='#7B68EE')




plt.xlabel('Features')
plt.title('Data Points and Fitted model')
plt.show()

From the collective graph we can see that almost all models gave similar results so we can use any model for our dataset.